Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	53×	body	1280	valid
4.0ms	39×	body	640	valid
4.0ms	129×	body	80	valid
2.0ms	27×	body	320	valid
0.0ms	8×	body	160	valid

simplify197.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	350
14	350
13	346
12	340
11	329
10	222
9	96
8	75
7	58
6	39
5	27
4	21
3	19
2	16
1	12
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

14.0ms	(/ x (+ x 1.0))
30.0ms	(/ (+ x 1.0) (- x 1.0))
105.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series253.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ x (+ x 1.0))
53.0ms	(/ (+ x 1.0) (- x 1.0))
159.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.0s

Counts

605 → 605

Iterations

Iter	Nodes
done	5013
2	3287
1	1251
0	523

prune2.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (* (* (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

2788×	`*-un-lft-identity`
2112×	`times-frac`
1660×	`add-sqr-sqrt`
1404×	`prod-diff`
1192×	`add-cube-cbrt`
537×	`distribute-lft-out`
270×	`associate-/r/`
255×	`distribute-lft-out--`
228×	`difference-of-squares`
135×	`div-inv`
105×	`flip3--` `flip--`
81×	`frac-times` `flip3-+` `flip-+`
63×	`cbrt-div`
54×	`fma-neg`
51×	`frac-sub`
27×	`associate-*l/`
15×	`associate-*r/`
10×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`sub-neg` `diff-log`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 1617

Calls

4 calls:

684.0ms	(cbrt (* (* (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
106.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
152.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
122.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (* (* (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
515.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
189.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
210.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.4s

Counts

1629 → 1629

Iterations

Iter	Nodes
done	5000
1	1630
0	700

prune6.8s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.4b	(/ 1.0 (* x x))
0.7b	(/ 3.0 (* (* x x) x))
10.3b	(+ (/ 1.0 (* x x)) (/ 3.0 (* (* x x) x)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
9×	`times-frac`
7×	`fma-def` `prod-exp` `cbrt-unprod`
6×	`pow-plus` `pow-prod-up` `associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `pow-prod-down` `div-inv`
2×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `associate-l` `pow3` `frac-add` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

21.0ms	(* (* x x) x)
9.0ms	(/ 1.0 (* x x))
22.0ms	(/ 3.0 (* (* x x) x))
39.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 (* (* x x) x)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (* x x) x)
38.0ms	(/ 1.0 (* x x))
58.0ms	(/ 3.0 (* (* x x) x))
128.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 (* (* x x) x)))

simplify1.1s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1222
1	347
0	133

prune361.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 3.0 x (fma (* x x) 1.0 1.0))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 3.0 x (fma (* x x) 1.0 1.0))

series37.0ms

Counts

1 → 3

Calls

1 calls:

37.0ms

(fma 3.0 x (fma (* x x) 1.0 1.0))

simplify2.6s

Counts

13 → 13

Iterations

Iter	Nodes
done	5000
4	3493
3	515
2	108
1	37
0	21

prune56.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

100% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 32.3b

bsearch151.0ms

Steps

Iters	Range		Point
11	3.4817375791661903e-26	573579.0075499975	1.021370211112824
10	-84463.33967257517	-3.2432757514909933e-09	-0.9983730585657322

simplify14.0ms

Iterations

Iter	Nodes
done	38
3	38
2	35
1	28
0	19

end0.0ms

sample1.6s

Algorithm

intervals

Results

616.0ms	4151×	body	80	valid
403.0ms	1644×	body	1280	valid
235.0ms	1270×	body	640	valid
76.0ms	297×	body	160	valid
76.0ms	638×	body	320	valid